Question

An electron makes a transition from an excited state to the ground state of a hydrogen-like atom. Then

• A. Kinetic energy decreases, potential energy increases but total energy remains same.
• B. Kinetic energy and total energy decrease but potential energy increases.
• C. Its kinetic energy increases but potential energy and total energy decrease.
• D. Kinetic energy, potential energy and total energy decrease.

Answer 1

Answer: (C)

We know that total energy $E$ , potential energy $U$ and kinetic energy $K$ in the $n^{th}$ orbit is given by
$E=-\frac{13.6z^2}{n^2}eV$ ,
$U=-2\times \frac{13.6z^2}{n^2}eV,K=\frac{13.6z^2}{n^2}eV$
$\therefore U=-2K=2E$
As the total energy decreases with decrease in $n$ , so potential energy decreases and kinetic energy increases with decrease in $n$ .
Hence, when an electron makes a transition from an excited state to the ground state of a hydrogen-like atom, then its kinetic energy increases but potential energy and total energy decrease.